Perturbation theory made efficient and effective for predictions of ionization potential and electron affinity

Ionization potential and electron affinity are essential molecular properties. The most straightforward method is to calculate them by taking the total energy differences of the initial and final states according to the definition. However, it often suffers from a serious convergence problem due to the requirement of the self-consistent field (SCF) calculations for the ionic states with non-Aufbau choices of occupations. In the present work, we have constructed a theoretical framework in view of perturbation theory to bypass the SCF calculations of the ionic states. To address the imbalance issue that arises from the precisely treated neutral ground state followed by the truncated perturbative treatment of the ionic states, an accurate yet effective method has been developed here, which adds back some terms from the higher order perturbations into the lower order to cancel out the most computationally cost terms in the truncated expansion, thus reaching a better convergence with less computation. The validity of the present methodology has been tested out by applying it to the Hartree-Fock (HF) method in combination with the correlation effect described at the second-order Møller-Plesset level in a frozen-orbital approximation. All the derivations in this work are given in a general framework, which are applicable not only to HF but also to a wide range of density functional theory methods from semi-local functionals to hybrid and doubly hybrid functionals.

Insights into Direct Methods for Predictions of Ionization Potential and Electron Affinity in Density Functional Theory

Vertical ionization potential (IP) and electron affinity (EA) are fundamental molecular properties, while the Δ method and the direct method are the widely used approaches to compute these properties. The Δ method is calculated by taking the total energy difference of the initial and final states, whose reliability is seriously affected by the issue associated with the imbalanced treatment of these two states. The direct method based on the derivatives involving only one single-state calculation can yield a quasi-particle spectrum whose accuracy, on the other hand, is mostly affected by the levels of approximate molecular structure theories. Because of the aforementioned issues, EA prediction can be particularly problematic. Here we present, for the first time, an analytic theory on the derivation and realization of generalized Kohn-Sham (KS) eigenvalues of doubly hybrid (DH) functionals that depend on both occupied and unoccupied orbitals. The method based on the KS eigenvalues of neutral systems, termed the NKS method, is found to suffer little from the imbalance issue, while it is only the NKS method that can offer accurate EA prediction from a good functional approximation, such as the XYG3 type of DH functionals. Being less sensitive to the size of basis sets, the NKS method is of great significance for its application to large systems. The insights gained in this work are useful for the calculation of properties associated with small energy differences while emphasizing the importance of the development of generalized functionals that rely on both occupied and unoccupied orbitals.

Dielectric Screening Meets Optimally Tuned Density Functionals

A short overview of recent attempts at merging two independently developed methods is presented. These are the optimal tuning of a range-separated hybrid (OT-RSH) functional, developed to provide an accurate first-principles description of the electronic structure and optical properties of gas-phase molecules, and the polarizable continuum model (PCM), developed to provide an approximate but computationally tractable description of a solvent in terms of an effective dielectric medium. After a brief overview of the OT-RSH approach, its combination with the PCM as a potentially accurate yet low-cost approach to the study of molecular assemblies and solids, particularly in the context of photocatalysis and photovoltaics, is discussed. First, solvated molecules are considered, with an emphasis on the challenge of balancing eigenvalue and total energy trends. Then, it is shown that the same merging of methods can also be used to study the electronic and optical properties of molecular solids, with a similar discussion of the pros and cons. Tuning of the effective scalar dielectric constant as one recent approach that mitigates some of the difficulties in merging the two approaches is considered.

Accurate description of the electronic structure of organic semiconductors by GW methods

Electronic properties associated with charged excitations, such as the ionization potential (IP), the electron affinity (EA), and the energy level alignment at interfaces, are critical parameters for the performance of organic electronic devices. To computationally design organic semiconductors and functional interfaces with tailored properties for target applications it is necessary to accurately predict these properties from first principles. Many-body perturbation theory is often used for this purpose within the GW approximation, where G is the one particle Green's function and W is the dynamically screened Coulomb interaction. Here, the formalism of GW methods at different levels of self-consistency is briefly introduced and some recent applications to organic semiconductors and interfaces are reviewed.

Solid state effects on the electronic structure of H2OEP

We present the results of a joint experimental and theoretical investigation concerning the effect of crystal packing on the electronic properties of the H2OEP molecule. Thin films, deposited in ultra high vacuum on metal surfaces, are investigated by combining valence band photoemission, inverse photoemission, and X-ray absorption spectroscopy. The spectra of the films are compared, when possible, with those measured in the gas phase. Once many-body effects are included in the calculations through the GW method, the electronic structure of H2OEP in the film and gas phase are accurately reproduced for both valence and conduction states. Upon going from an isolated molecule to the film phase, the electronic gap shrinks significantly and the lowest unoccupied molecular orbital (LUMO) and LUMO + 1 degeneracy is removed. The calculations show that the reduction of the transport gap in the film is entirely addressable to the enhancement of the electronic screening.

Quantitative analysis of valence photoemission spectra and quasiparticle excitations at chromophore-semiconductor interfaces

Investigating quasiparticle excitations of molecules on surfaces through photoemission spectroscopy forms a major part of nanotechnology research. Resolving spectral features at these interfaces requires a comprehensive theory of electron removal and addition processes in molecules and solids which captures the complex interplay of image charges, thermal effects, and configurational disorder. Here, we develop such a theory and calculate the quasiparticle energy-level alignment and the valence photoemission spectrum for the prototype biomimetic solar cell interface between anatase TiO(2) and the N3 chromophore. By directly matching our calculated photoemission spectrum to experimental data, we clarify the atomistic origin of the chromophore peak at low binding energy. This case study sets a new standard in the interpretation of photoemission spectroscopy at complex chromophore-semiconductor interfaces.

Valence structures of aromatic bioactive compounds: a combined theoretical and experimental study

Valence electronic structures of three recently isolated aryl bioactive compounds, namely 2-phenylethanol (2PE), p-hydroxyphenylethanol (HPE) and 4-hydroxybenzaldehyde (HBA), are studied using a combined theoretical and experimental method. Density functional theory-based calculations indicate that the side chains cause electron charge redistribution and therefore influence the aromaticity of the benzene derivatives. The simulated IR spectra further reveal features induced by the side chains. Solvent effects on the IR spectra are simulated using the polarizable continuum model, which exhibits enhancement of the O-H stretch vibrations with significant red-shift of 464 cm(-1) in 2PE. A significant spectral peak splitting of 94 cm(-1) between O(4)-H and O(8)-H of HPE is revealed in an aqueous environment. Experimental measurements for valence binding energy spectra for 2PE, HPE and HBA are presented and analyzed using outer-valence Green function calculations. The experimental (predicted) first ionization energies are measured as 9.19 (8.79), 8.47 (8.27) and 8.97 (8.82) eV for 2PE, HPE and HBA, respectively. The frontier orbitals (highest occupied molecular orbitals, HOMOs, and lowest unoccupied molecular orbitals, LUMOs) have similar atomic orbital characters although the HOMO-LUMO energy gaps are quite different.

Excitation Gaps of Finite-Sized Systems from Optimally Tuned Range-Separated Hybrid Functionals

Excitation gaps are of considerable significance in electronic structure theory. Two different gaps are of particular interest. The fundamental gap is defined by charged excitations, as the difference between the first ionization potential and the first electron affinity. The optical gap is defined by a neutral excitation, as the difference between the energies of the lowest dipole-allowed excited state and the ground state. Within many-body perturbation theory, the fundamental gap is the difference between the corresponding lowest quasi-hole and quasi-electron excitation energies, and the optical gap is addressed by including the interaction between a quasi-electron and a quasi-hole. A long-standing challenge has been the attainment of a similar description within density functional theory (DFT), with much debate on whether this is an achievable goal even in principle. Recently, we have constructed and applied a new approach to this problem. Anchored in the rigorous theoretical framework of the generalized Kohn-Sham equation, our method is based on a range-split hybrid functional that uses exact long-range exchange. Its main novel feature is that the range-splitting parameter is not a universal constant but rather is determined from first principles, per system, based on satisfaction of the ionization potential theorem. For finite-sized objects, this DFT approach mimics successfully, to the best of our knowledge for the first time, the quasi-particle picture of many-body theory. Specifically, it allows for the extraction of both the fundamental and the optical gap from one underlying functional, based on the HOMO-LUMO gap of a ground-state DFT calculation and the lowest excitation energy of a linear-response time-dependent DFT calculation, respectively. In particular, it produces the correct optical gap for the difficult case of charge-transfer and charge-transfer-like scenarios, where conventional functionals are known to fail. In this perspective, we overview the formal and practical challenges associated with gap calculations, explain our new approach and how it overcomes previous difficulties, and survey its application to a variety of systems.